A Gaussian Mixture Model (GMM). More...

#include <gmm.hpp>

Public Member Functions
	GMM ()
	Create an empty Gaussian Mixture Model, with zero gaussians.

	GMM (const size_t gaussians, const size_t dimensionality)
	Create a GMM with the given number of Gaussians, each of which have the specified dimensionality. More...

	GMM (const std::vector< distribution::GaussianDistribution > &dists, const arma::vec &weights)
	Create a GMM with the given dists and weights. More...

	GMM (const GMM &other)
	Copy constructor for GMMs.

GMM &	operator= (const GMM &other)
	Copy operator for GMMs.

size_t	Gaussians () const
	Return the number of gaussians in the model.

size_t	Dimensionality () const
	Return the dimensionality of the model.

const distribution::GaussianDistribution &	Component (size_t i) const
	Return a const reference to a component distribution. More...

distribution::GaussianDistribution &	Component (size_t i)
	Return a reference to a component distribution. More...

const arma::vec &	Weights () const
	Return a const reference to the a priori weights of each Gaussian.

arma::vec &	Weights ()
	Return a reference to the a priori weights of each Gaussian.

double	Probability (const arma::vec &observation) const
	Return the probability that the given observation came from this distribution. More...

void	Probability (const arma::mat &observation, arma::vec &probs) const
	Return the probability of the given observation matrix. More...

double	LogProbability (const arma::vec &observation) const
	Return the log probability that the given observation came from this distribution. More...

void	LogProbability (const arma::mat &observation, arma::vec &logProbs) const
	Return the log-probability of the given observation (x) matrix. More...

double	Probability (const arma::vec &observation, const size_t component) const
	Return the probability that the given observation came from the given Gaussian component in this distribution. More...

double	LogProbability (const arma::vec &observation, const size_t component) const
	Return the log probability that the given observation came from the given Gaussian component in this distribution. More...

arma::vec	Random () const
	Return a randomly generated observation according to the probability distribution defined by this object. More...

template<typename FittingType = EMFit<>>
double	Train (const arma::mat &observations, const size_t trials=1, const bool useExistingModel=false, FittingType fitter=FittingType())
	Estimate the probability distribution directly from the given observations, using the given algorithm in the FittingType class to fit the data. More...

template<typename FittingType = EMFit<>>
double	Train (const arma::mat &observations, const arma::vec &probabilities, const size_t trials=1, const bool useExistingModel=false, FittingType fitter=FittingType())
	Estimate the probability distribution directly from the given observations, taking into account the probability of each observation actually being from this distribution, and using the given algorithm in the FittingType class to fit the data. More...

void	Classify (const arma::mat &observations, arma::Row< size_t > &labels) const
	Classify the given observations as being from an individual component in this GMM. More...

template<typename Archive >
void	serialize (Archive &ar, const uint32_t)
	Serialize the GMM. More...

Detailed Description

A Gaussian Mixture Model (GMM).

This class uses maximum likelihood loss functions to estimate the parameters of the GMM on a given dataset via the given fitting mechanism, defined by the FittingType template parameter. The GMM can be trained using normal data, or data with probabilities of being from this GMM (see GMM::Train() for more information).

The Train() method uses a template type 'FittingType'. The FittingType template class must provide a way for the GMM to train on data. It must provide the following two functions:

void Estimate(const arma::mat& observations,
              std::vector<distribution::GaussianDistribution>& dists,
              arma::vec& weights);
void Estimate(const arma::mat& observations,
              const arma::vec& probabilities,
              std::vector<distribution::GaussianDistribution>& dists,
              arma::vec& weights);

These functions should produce a trained GMM from the given observations and probabilities. These may modify the size of the model (by increasing the size of the mean and covariance vectors as well as the weight vectors), but the method should expect that these vectors are already set to the size of the GMM as specified in the constructor.

For a sample implementation, see the EMFit class; this class uses the EM algorithm to train a GMM, and is the default fitting type for the Train() method.

The GMM, once trained, can be used to generate random points from the distribution and estimate the probability of points being from the distribution. The parameters of the GMM can be obtained through the accessors and mutators.

Example use:

// Set up a mixture of 5 gaussians in a 4-dimensional space.
GMM g(5, 4);
// Train the GMM given the data observations, using the default EM fitting
// mechanism.
g.Train(data);
// Get the probability of 'observation' being observed from this GMM.
double probability = g.Probability(observation);
// Get a random observation from the GMM.
arma::vec observation = g.Random();

Constructor & Destructor Documentation

◆ GMM() [1/2]

mlpack::gmm::GMM::GMM	(	const size_t	gaussians,
		const size_t	dimensionality
	)

Create a GMM with the given number of Gaussians, each of which have the specified dimensionality.

The means and covariances will be set to 0.

Parameters

gaussians	Number of Gaussians in this GMM.
dimensionality	Dimensionality of each Gaussian.

◆ GMM() [2/2]

mlpack::gmm::GMM::GMM	(	const std::vector< distribution::GaussianDistribution > &	dists,
		const arma::vec &	weights
	)

inline

Create a GMM with the given dists and weights.

Parameters

dists	Distributions of the model.
weights	Weights of the model.

Member Function Documentation

◆ Classify()

void mlpack::gmm::GMM::Classify	(	const arma::mat &	observations,
		arma::Row< size_t > &	labels
	)		const

Classify the given observations as being from an individual component in this GMM.

The resultant classifications are stored in the 'labels' object, and each label will be between 0 and (Gaussians() - 1). Supposing that a point was classified with label 2, and that our GMM object was called 'gmm', one could access the relevant Gaussian distribution as follows:

arma::vec mean = gmm.Means()[2];
arma::mat covariance = gmm.Covariances()[2];
double priorWeight = gmm.Weights()[2];

Parameters

observations	List of observations to classify.
labels	Object which will be filled with labels.
observation	Observation matrix for classification.
labels	Save the labels for the given observation matrix.

◆ Component() [1/2]

const distribution::GaussianDistribution& mlpack::gmm::GMM::Component ( size_t i ) const

inline

Return a const reference to a component distribution.

Parameters

i	Index of component.

◆ Component() [2/2]

distribution::GaussianDistribution& mlpack::gmm::GMM::Component ( size_t i )

inline

Return a reference to a component distribution.

Parameters

i	Index of component.

◆ LogProbability() [1/3]

double mlpack::gmm::GMM::LogProbability ( const arma::vec & observation ) const

Return the log probability that the given observation came from this distribution.

Return the log probability of the given observation being from this GMM.

Parameters

observation	Observation vector to evaluate the probability of.
observation	Observation vector to compute log-probabilty.

◆ LogProbability() [2/3]

void mlpack::gmm::GMM::LogProbability	(	const arma::mat &	observation,
		arma::vec &	logProbs
	)		const

Return the log-probability of the given observation (x) matrix.

Return the log probability of the given observation GMM matrix.

Parameters

observation	Observation matrix.
logProbs	Vector to store log-probability value of observation.
observation	Observation matrix to compute log-probabilty.
logProbs	Stores the value of log-probability for Observation.

◆ LogProbability() [3/3]

double mlpack::gmm::GMM::LogProbability	(	const arma::vec &	observation,
		const size_t	component
	)		const

Return the log probability that the given observation came from the given Gaussian component in this distribution.

Return the log probability of the given observation being from the given component in the mixture.

Parameters

observation	Observation to evaluate the probability of.
component	Index of the component of the GMM to be considered.
observation	Observation vector to compute log-probabilty.
component	Calculate the log-probability for given observation vector.

◆ Probability() [1/3]

double mlpack::gmm::GMM::Probability ( const arma::vec & observation ) const

Return the probability that the given observation came from this distribution.

Return the probability of the given observation being from this GMM.

Parameters

observation	Observation vector to evaluate the probability of.
observation	Observation vector to compute probabilty.

◆ Probability() [2/3]

void mlpack::gmm::GMM::Probability	(	const arma::mat &	observation,
		arma::vec &	probs
	)		const

Return the probability of the given observation matrix.

Return the probability of the given observation GMM matrix.

Parameters

observation	Observation matrix.
probs	Vector to store probability value of observation x.
observation	Observation matrix to compute probabilty.
probs	Stores the value of probability for x.

◆ Probability() [3/3]

double mlpack::gmm::GMM::Probability	(	const arma::vec &	observation,
		const size_t	component
	)		const

Return the probability that the given observation came from the given Gaussian component in this distribution.

Return the probability of the given observation being from the given component in the mixture.

Parameters

observation	Observation to evaluate the probability of.
component	Index of the component of the GMM to be considered.
observation	Observation matrix to compute probabilty.
component	Calculate the probability for given component.

◆ Random()

arma::vec mlpack::gmm::GMM::Random ( ) const

Return a randomly generated observation according to the probability distribution defined by this object.

Returns: Random observation from this GMM.

◆ serialize()

template<typename Archive >

void mlpack::gmm::GMM::serialize	(	Archive &	ar,
		const uint32_t
	)

Serialize the GMM.

Serialize the object.

◆ Train() [1/2]

template<typename FittingType >

double mlpack::gmm::GMM::Train	(	const arma::mat &	observations,
		const size_t	trials = `1`,
		const bool	useExistingModel = `false`,
		FittingType	fitter = `FittingType()`
	)

Estimate the probability distribution directly from the given observations, using the given algorithm in the FittingType class to fit the data.

Fit the GMM to the given observations.

The fitting will be performed 'trials' times; from these trials, the model with the greatest log-likelihood will be selected. By default, only one trial is performed. The log-likelihood of the best fitting is returned.

Optionally, the existing model can be used as an initial model for the estimation by setting 'useExistingModel' to true. If the fitting procedure is deterministic after the initial position is given, then 'trials' should be set to 1.

Template Parameters

FittingType The type of fitting method which should be used (EMFit<> is suggested).

Parameters

observations	Observations of the model.
trials	Number of trials to perform; the model in these trials with the greatest log-likelihood will be selected.
useExistingModel	If true, the existing model is used as an initial model for the estimation.
fitter	The fitter to use, optional.

Returns: The log-likelihood of the best fit.

◆ Train() [2/2]

template<typename FittingType >

double mlpack::gmm::GMM::Train	(	const arma::mat &	observations,
		const arma::vec &	probabilities,
		const size_t	trials = `1`,
		const bool	useExistingModel = `false`,
		FittingType	fitter = `FittingType()`
	)

Estimate the probability distribution directly from the given observations, taking into account the probability of each observation actually being from this distribution, and using the given algorithm in the FittingType class to fit the data.

Fit the GMM to the given observations, each of which has a certain probability of being from this distribution.

The fitting will be performed 'trials' times; from these trials, the model with the greatest log-likelihood will be selected. By default, only one trial is performed. The log-likelihood of the best fitting is returned.

Optionally, the existing model can be used as an initial model for the estimation by setting 'useExistingModel' to true. If the fitting procedure is deterministic after the initial position is given, then 'trials' should be set to 1.

Parameters

observations	Observations of the model.
probabilities	Probability of each observation being from this distribution.
trials	Number of trials to perform; the model in these trials with the greatest log-likelihood will be selected.
useExistingModel	If true, the existing model is used as an initial model for the estimation.
fitter	The fitter to use, optional.

Returns: The log-likelihood of the best fit.

The documentation for this class was generated from the following files:

src/mlpack/methods/gmm/gmm.hpp
src/mlpack/methods/gmm/gmm.cpp
src/mlpack/methods/gmm/gmm_impl.hpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ GMM() [1/2]

◆ GMM() [2/2]

Member Function Documentation

◆ Classify()

◆ Component() [1/2]

◆ Component() [2/2]

◆ LogProbability() [1/3]

◆ LogProbability() [2/3]

◆ LogProbability() [3/3]

◆ Probability() [1/3]

◆ Probability() [2/3]

◆ Probability() [3/3]

◆ Random()

◆ serialize()

◆ Train() [1/2]

◆ Train() [2/2]